Dekrét, Anton; Bakša, Ján Applications of line objects in robotics. (English) Zbl 1046.70004 Acta Univ. M. Belii, Ser. Math. 9, 29-42 (2001). Summary: The Lie algebra of Lie group of Euclidean motions in \(E_3\) is represented as the vector space \(A_6\) of couples of vectors in \(E_3\). We describe all subalgebras and all 3-dimensional subspaces of \(A_6\) which are orthogonal to themselves according to the Klein form, and give their kinematic interpretations. Vector fields in \(E_3\) determined by elements of \(A_6\) and their kinematic and dynamic interpretations are investigated. Cited in 1 Document MSC: 70B15 Kinematics of mechanisms and robots 70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics 22E70 Applications of Lie groups to the sciences; explicit representations Keywords:Lie algebra; Lie group; Euclidean motions; Klein form PDF BibTeX XML Cite \textit{A. Dekrét} and \textit{J. Bakša}, Acta Univ. M. Belii, Ser. Math. 9, 29--42 (2001; Zbl 1046.70004)